A volume V of a viscous liquid flows per unit time due to a pressure head `DeltaP` along a pipe of diameter d and length l. instead of this pipe a set of four pipes each of diameter `(d)/(2)` and length 2l is connected to the same pressure head `DeltaP`. Now the volume of liquid flowing per unit time is:

Options

A. `(V)/(16)`
B. `(V)/(8)`
C. `(V)/(4)`
D. `V`

Answer

B

Explanation

`V=(piPr^(4))/(8 l eta),Vprop(r^(4))/(l)`
`(V_(1))/(V_(2))=((r_(1))/(r_(2)))^(4)xx(l_(2))/(l_(1))=32,V_(2)=(V)/(32)`
For 4 pipes,
`V_(2)^(1)=4V_(2)=4xx(V)/(32)=(V)/(8)`